Hard-Thermal-Loop Corrections in Leptogenesis I: CP-Asymmetries

We investigate hard-thermal-loop (HTL) corrections to the CP-asymmetries in neutrino and, at high temperature, Higgs boson decays in leptogenesis. We pay special attention to the two leptonic quasiparticles that arise at non-zero temperature and find that there are four contributions to the CP-asymmetries, which correspond to the four combinations of the two leptonic quasiparticles in the loop and in the final states. In two additional cases, we approximate the full HTL-lepton propagator with a zero-temperature propagator that employs the thermal lepton mass m_l(T), or the asymptotic thermal lepton mass sqrt{2} m_l(T). We find that the CP-asymmetries in the one-mode approaches differ by up to one order of magnitude from the full two-mode treatment in the interesting temperature regime T \sim M_1. The asymmetry in Higgs boson decays turns out to be two orders of magnitude larger than the asymmetry in neutrino decays in the zero-temperature treatment. The effect of HTL corrections on the final lepton asymmetry are investigated in paper II of this series.